A short and elementary proof of the main Bahadur-Kiefer theorem

DOI10.1214/aop/1042644730zbMath0897.62046OpenAlexW2034146512MaRDI QIDQ1922092

John H. J. Einmahl

Publication date: 12 September 1996

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1042644730

zbMATH Keywords

strong lawempirical processeslower boundquantile processBahadur-Kiefer process

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items (4)

Information bounds for nonparametric estimators of \(L\)-functionals and survival functionals under censored data ⋮ Inference for asymptotically independent samples of extremes ⋮ Asymptotic behavior of central order statistics from stationary processes ⋮ On the Bahadur representation of sample quantiles for dependent sequences

Cites Work

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• Bahadur-Kiefer-type processes
• The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
• The oscillation behavior of empirical processes
• Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator
• Kiefer's theorem via the Hungarian construction
• Strong limit theorems for oscillation moduli of the uniform empirical process
• A Note on Quantiles in Large Samples
• An inequality involving multinomial probabilities

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